To fact check is to evaluate someone’s statement for its truthfulness. Factcheck.org is a website that evaluates political claims that is run by the University of Pennsylvania.
See this article on misleading statements about gasoline prices by politicians on both sides of the aisle, for instance:
To fact check you must first identify which factual claims are made by a speaker or writer. Then you must research and determine the truth of the matter. Finally, you write up your evaluation. Are the statements made factual or are they misrepresentations?
In terms of how you present your analysis of Dr. Boyd’s claim, there is some room for creativity. But you must first identify which statements you wish to fact check. Often you will need to re-write the statements to highlight the factual issue. (i.e. you may want to quantify vague statements or made apparent any facts omitted over oversimplified by the speaker).
Then present your research and assess whether it supports or undermines the statements you are fact checking.